I have simple lesson with 3 cards. Each card - essay, so I have three essays in one lesson. When I try to grade 3 essays as a teacher, I can see only one (!), the first essay in completed essays list, but I know that student completed all the 3 essays.

Hmmm... I couldn't reproduce your problem. You did click on the "Grade essay questions (X not graded and X not sent)" link right? Also, essays do not appear for grading unless the student actually finishes the Lesson by going to the end of the Lesson. I would also suggest creating a test student account and take the lesson as the test student and see if the essays appear or not.

We are currently having exactly this problem. We have two essays and no other question types in this particular lesson and we can only see a single essay for most students yet we know that they completed both.

Found a bug in the essay view code. A fix is in MOODLE_15_STABLE and HEAD. You will have to wait for the code to repackage itself for download to be able to get the fix. Attached is a diff file if you want to make the change yourself. The change is very minor; at two places you need to move a single line down a couple of lines in /mod/lesson/view.php.